The conical-channel flow of a dilute polymer solution is investigated theoretically. The stress field due to polymer additive is calculated using a new molecular model, based on the physical picture of the polymer molecules unravelling in strong flows and Batchelor's theory for the stress in a suspension of elongated particles. Good agreement is obtained with the experimental results of James & Saringer (1980). The absence of a significant polymer effect in a two-dimensional case (the wedge-channel flow), observed by the same authors (James & Saringer 1982a), is also explained. The fundamental differences between the proposed model and the elastic-dumbbell models are discussed.

Large-amplitude waves can exist on an air-water interface where the air is in steady non-uniform flow and the water is stationary. Computations of such waves are provided here, both for periodic nonlinear Stokes-like waves, and for a specific wave-making configuration in which the periodic solution appears as the downstream far field. The wavemaker geometry chosen here is relevant to the edge region of a hovercraft, and the large-amplitude free-surface disturbance caused by the escaping air is computed as a function of the Froude number based on air-jet velocity and thickness.

The commonly used linear K-l and K-ε models of turbulence are shown to be incapable of accurately predicting turbulent flows where the normal Reynolds stresses play an important role. By means of an asymptotic expansion, nonlinear K-l and K-ε models are obtained which, unlike all such previous nonlinear models, satisfy both realizability and the necessary invariance requirements. Calculations are presented which demonstrate that this nonlinear model is able to predict the normal Reynolds stresses in turbulent channel flow much more accurately than the linear model. Furthermore, the nonlinear model is shown to be capable of predicting turbulent secondary flows in non-circular ducts - a phenomenon which the linear models are fundamentally unable to describe. An additional application of this model to the improved prediction of separated flows is discussed briefly along with other possible avenues of future research.

The effect of free-stream turbulence on the mean pressure distribution along the separation bubble formed on a flat plate with rectangular leading-edge geometry is investigated experimentally in a wind tunnel using turbulence-producing grids. Emphasis is placed on finding the effect of turbulence scale. The ratio of turbulence scale to plate thickness investigated was about 0.5 to 24 for two values of turbulence intensity of about 7 and 11%. The Reynolds number based on plate thickness was approximately (1.4–4.2) × 104.

It is found that the main effect of free-stream turbulence is to shorten the separation bubble. It is progressively shortened with increasing turbulence intensity. The mean pressure distribution along the shortened separation bubble is insensitive to changing turbulence scale up to a scale ratio of about 2. With further increase in the scale ratio it asymptotes towards the smooth-flow distribution. There is no trace of interaction between turbulence and vortex shedding (the impinging-shear-layer instability) in the mean pressure distribution.

We consider finite-amplitude thermal convection, in a horizontal fluid layer. The viscosity of the fluid is dependent upon its temperature. Using a weakly nonlinear expansion procedure, we examine the stability of two-dimensional roll and three-dimensional square planforms, in order to determine which should be preferred in convection experiments. The analysis shows that the roll planform is preferred for low values of the ratio of the viscosities at the top and bottom boundaries, but the square planform is preferred for larger values of the ratio. At still larger values, subcritical convection is predicted. We also include the effects of boundaries having finite thermal conductivity, which enables favourable comparison to be made with experimental studies. A discrepancy between the present work and a previous study of this problem (Busse & Frick 1985) is discussed.

A simple mathematical model for the flow in a conical cyclone is developed which allows solutions to be obtained in closed form. The flow in the main body of the cyclone is regarded as inviscid but the nature of the fluid entry to the device and the conical geometry ensure that secondary flows develop which make the flow highly rotational. The results of the theory are compared with data from two quite different experimental investigations, and good agreement is obtained.

We investigate the dynamical consequences of an axisymmetric velocity field with a poloidal magnetic field driven by a prescribed e.m.f. E. The problem is motivated by previous investigations of dynamically driven dynamos in the magnetostrophic range. A geostrophic zonal flow field is added to a previously described velocity, and determined by the requirement that Taylor's constraint (Taylor 1963) (guaranteeing dynamical self-consistency of the fields) be satisfied. Several solutions are exhibited, and it is suggested that self-consistent solutions can always be found to this ‘forced’ problem, whereas the usual α-effect dynamo formalism in which E is a linear function of the magnetic field leads to a difficult transcendentally nonlinear characteristic value problem that may not always possess solutions.

The general solution for low-Reynolds-number flow about an ellipsoid is derived by the singularity method and by representation in ellipsoidal harmonics. It is shown that, as in potential flow, the focal ellipse is the image system for the ellipsoid. A simple transformation which resembles a step in the derivation of the Dirichlet potential is introduced and its implications are explored. This transformation converts the velocity representation for an nth-order ambient field into that for the (n + 1)th-order field. The method furnishes an explanation for the invariance of the domain of the singularity distribution (the focal ellipse) with respect to the ambient field. Faxén relations for all multipole moments for arbitrary Stokes flow are derived in both integral and symbolic operator forms.

The inviscid instability of a columnar trailing-line vortex at large values of the azimuthal wavenumber n near neutral conditions is considered. This extends an earlier analysis (Leibovich & Stewartson 1983), which is not accurate near the limiting values of the axial wavenumber for which instabilities exist. Here an asymptotic expansion is derived for the solution in the neighbourhood of the lower neutral point and the results compared with existing computations a t moderate values of n. For these weak instabilities disturbances are centred near the axis of the vortex and the relevant equation is solved in the complex plane by a generalized saddle-point method. In addition, the marginal stability of the vortex is examined, and an estimate obtained of the value of the swirl parameter above which the vortex is stable at large values of n.